Latex terms

#concept-pamphlet

What is the LaTeX code for the greater than or equal to symbol? ? \geq

$$\ge$$

What is the LaTeX code for the less than or equal to symbol? ? \leq

$$\le$$

What is the LaTeX code for the not equal to symbol? ? \neq

$$\ne$$

What is the LaTeX code for the approximately equal to symbol? ? \approx

$$\approx$$

What is the LaTeX code for the tilde symbol? ? \sim

$$\sim$$

What is the LaTeX code for the right arrow symbol? ? \Rightarrow

$$\Rightarrow$$

What is the LaTeX code for the square root of 42? ? \sqrt{42}

$$\sqrt{42}$$

What is the LaTeX code for the infinity symbol? ? \infty

$$\infty$$

What is the LaTeX code for this symbol?

$$\lambda$$

? \lambda

What is the LaTeX code for these symbols?

$$\mu ,\sigma$$

? \mu, \sigma

What is the LaTeX code for this symbol?

$$\Phi (0)$$

? \Phi(0)

What is the LaTeX code for the this symbol?

$$\Sigma$$

? \Sigma

What is the LaTeX code for this symbol?

$$\theta$$

? \theta

What is the LaTeX code for the bar X and hat X symbols?

$$\bar{X},\hat{X}$$

? \bar{X}, \hat{X}

What is the LaTeX code for the dots here:

$$1,2,\cdots ,n$$

? \cdots

What is the LaTeX code for verbatim text ‘my_function()’? ? \verb|my_function()|

\verb|my_function()|$$ <!--LEARN:D4lJwS8N--> What is the LaTeX code for a fraction with units in the numerator and denominator? ? `\frac{1}{1}`

\frac{1}{2}$$

What is the LaTeX code for summation from i equals 0 to n? ? \sum_{i=0}^{n} i

What is the LaTeX code for product from i equals 0 to n? ? \prod_{i=0}^{n} i

What is the LaTeX code for the probability of A intersect B? ? P(A \cap B)$$ P(A \cap B)

<!--LEARN:ZU2D4QYv--> What is the LaTeX code for the probability of A union B? ? `P(A \cup B)` $$P(A \cup B)

What is the LaTeX code for the binomial coefficient? ? \binom{n}{k}

^This is n! / ( k! (n-k)! ). Also pronounced “n choose k”. Also seen as C(n,k)

What is the LaTeX code for the conditional probability of A given B complement? ? P(A|B^C)$$ P(A|B^C)

$$ComplementisallprobabilitiesnotinB<!--LEARN:HaRlAHgT-->WhatistheLaTeXcodefortheprobabilityofmeowgivencat??‘P(\text{meow }|\text{ cat})‘$$

P(\textrm{meow } | \textrm{ cat})

$$WhatistheLaTeXcodefortheprobabilityofaconditionlessthanorequalto5.0??‘P(\text{cond}\le 5.0)‘$$

P(\textrm{cond} \leq 5.0)

$$WhatistheLaTeXcodeforAtimesB??‘A\times B‘$$

A \times B

$$<!--LEARN:Wayfcc0B-->WhatistheLaTeXcodeforaNormalrandomvariableXwithmean0andvariance1??‘X\sim \mathcal{N}(\mu =0,{\sigma }^2=1)‘$$

X \sim \mathcal{N}(\mu = 0, \sigma^2 = 1)

$$<!--LEARN:jlQkdL7L-->WhatistheLaTeXcodeforanintegralfrom-1to1ofxsquareddx??‘{\int }_{-1}^1{x}^{2}dx‘$$

\int_{-1}^{1} x^2 - 2x + 1 dx

$$<!--LEARN:nnkpPSpc-->WhatistheLaTeXcodefortheevaluationoftheintegralfrom-1to1ofxsquareddx,withbrackets??‘{\left[x^2\right]}_{-1}^1‘$$

\left[ x^2 \right]_{-1}

$$<!--LEARN:0BBZOJLM-->WhatistheLaTeXcodeforadoubleintegral??‘\iint ‘‘{\iint }_0^{1}xydydx‘$$

\iint_{0}^{1} xy dy dx$$ What is the LaTeX code for the evaluation of a double integral? ? \left. expression \right|_{0}^{1} Example:\left. \frac{3}{4}y^2 \right|_{-1}^{x}`

$${\frac{2}{3}y|}_{-1}^x$$

What is the LaTeX code for a 2x2 matrix with elements a, b, c, and d?

$$\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$$

? \begin{bmatrix} a & b \\ c & d \end{bmatrix} What is the LaTeX code for the correlation coefficient?

$$\rho$$

? \rho

What is the LaTeX code for a group of equations aligned? ? \begin{align*, &=, \\, end{align*} Example:

\begin{align*} 
P(X=x|Y=1,W=P_1)  &= \frac{P(X=x,Y=1 | W=P_1)}{P(Y=1|W=P_1)} \\ 
&= P(X=x|W=P_1) \\ 
&= \binom{5}{x}(0.1)^x(0.9)^{5-x} \\ 
P(X=x|Y=1,W=P_2)  
&= \frac{P(X=x,Y=1 | W=P_2)}{P(Y=1|W=P_2)} \\ 
&= P(X=x|W=P_2) \\ 
&= \binom{5}{x}(0.1)^x(0.9)^{5-x} 
\end{align*}

$$\begin{array}{rl}P(X=x|Y=1,W=P_1)& =\frac{P(X=x,Y=1|W=P_1)}{P(Y=1|W=P_1)}\\ & =P(X=x|W=P_1)\\ & =\left(\genfrac{}{}{0ex}{}{5}{x}\right)(0.1{)}^x(0.9{)}^{5-x}\\ P(X=x|Y=1,W=P_2)& =\frac{P(X=x,Y=1|W=P_2)}{P(Y=1|W=P_2)}\\ & =P(X=x|W=P_2)\\ & =\left(\genfrac{}{}{0ex}{}{5}{x}\right)(0.1{)}^x(0.9{)}^{5-x}\end{array}$$

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Other cards that are cool but don’t need to be reviewed §

What is the LaTeX code for a Bernoulli random variable X with parameter p?

X \sim \textrm{Ber}(p)

$$X\sim \text{Ber}(p)$$

What is the LaTeX code for a Binomial random variable X with parameters n and p?

X \sim \textrm{Bin}(n,p)

$$X\sim \text{Bin}(n,p)$$

What is the LaTeX code for a Poisson random variable X with lambda equal to 0?

X \sim \textrm{Poi}(\lambda=0)

$$X\sim \text{Poi}(\lambda =0)$$

What is the LaTeX code for an Exponential random variable X with lambda equal to 0?

X \sim \textrm{Exp}(\lambda=0)

$$X\sim \text{Exp}(\lambda =0)$$

What is the LaTeX code for a Beta random variable theta with parameters a and b?

\theta \sim \textrm{Beta}(a,b)

$$\theta \sim \text{Beta}(a,b)$$

What is the LaTeX code for a double integral from 0 less than y less than x less than 1 of x over y dy dx?

\iint_{0<y<x<1} \frac{x}{y} dy dx

$${\iint }_{0<y<x<1}\frac{x}{y}dydx$$

What is the LaTeX code for the evaluation of a double integral from 0 less than y less than x less than 1 of x over y dy dx?

\left. \frac{2}{3}y - \frac{3}{4}y^2 \right|_{-1}^{x}

$${\frac{2}{3}y-\frac{3}{4}{y}^2|}_{-1}^x$$

What is the LaTeX code for the variance of X?

\textrm{Var}(X)

$$\text{Var}(X)$$

What is the LaTeX code for the covariance of X and Y?

\textrm{Cov}(X,Y)

$$\text{Cov}(X,Y)$$

Latex playground §

equation editor: https://editor.codecogs.com/ cheatsheet: https://wch.github.io/latexsheet/latexsheet.pdf another cheatsheet: (source) latex cheatsheet.pdf

> [!theorem] Title
> 
> Content

> [!corollary]
> 
> Content

Title

Content

Title

Content

> [!thm] Title
> 
> Content

> [!cor]
> 
> Content

Title

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Note

Content> [!thm] Title Content

Note

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Environment name	Alias
axiom	axm
definition	def
lemma	lem
proposition	prp
theorem	thm
corollary	cor
claim	clm
assumption	asm
example	exm
exercise	exr
conjecture	cnj
hypothesis	hyp
remark	rmk

$$\begin{array}{rl}a& =b\\ & =c\end{array}$$